The proposed RELEVAGAN is based on EVAGAN, which is an improved version of ACGAN. ACGAN's \(\mathcal {D}\) , along with differentiating between real or fake samples, also considers the class labels in the training process [1]}. That said, \(\mathcal {D}\)  of ACGAN works as a dual classifier for differentiating between the real/fake data and different classes of the input samples, whether coming from the real source or the \(\mathcal {G}\) . In addition to random noise samples \(z\) , the input of \(\mathcal {G}\)  in ACGAN includes class labels \(c\) . The generator of the ACGAN can generate the specified class data for which the labels are fed to its \(\mathcal {G}\) . The objective function of ACGAN can be derived using likelihoods denoted by \(L_S\)  and \(L_C\)  for the correct source data and real class labels, respectively. \(\mathcal {D}\)  trains to maximise \(L_{C} + L_{S}\)  and \(\mathcal {G}\)  learns to maximise \(L_{C} - L_{S}\) . Hence, the objective of \(\mathcal {D}\)  is to improve the two likelihoods, while the aim of \(\mathcal {G}\)  is to assist \(\mathcal {D}\)  in improving the performance on class labels. \(\mathcal {G}\) 's other target is to suppress the log-likelihood of \(\mathcal {D}\)  on fake samples. The \(\mathcal {D}\)  outputs probability distributions over sources and the class labels [\(P (S | \mathcal {X}), P (C | \mathcal {X})] = \mathcal {D}(\mathcal {X})\)  where \(S\)  denotes the sources (real/fake) and \(C\)  represents the class labels. Equations REF  and REF  represent the \(L_s\)  and \(L_c\)  respectively.
\( \begin{aligned}L_{S} = \mathbb {E}[log P (S = real | \mathcal {X}_{real} )]\ + \\\mathbb {E}[log P (S = fake | \mathcal {X}_{fake} )]\end{aligned}\) 
\( \begin{aligned}L_{C} = \mathbb {E}[log P (C = c| \mathcal {X}_{real} )]\ + \\\mathbb {E}[log P (C = c | \mathcal {X}_{fake} )]\end{aligned}\) 
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